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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A priori degeneracy of one-dimensional rotation sets for periodic point free torus maps
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by Jaroslaw Kwapisz PDF
Trans. Amer. Math. Soc. 354 (2002), 2865-2895

Abstract:

Diffeomorphisms of the two torus that are isotopic to the identity have rotation sets that are convex compact subsets of the plane. We show that certain line segments (including all rationally sloped segments with no rational points) cannot be realized as a rotation set.
References
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Additional Information
  • Jaroslaw Kwapisz
  • Affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717-2400
  • Email: jarek@math.montana.edu
  • Received by editor(s): January 10, 2001
  • Received by editor(s) in revised form: August 31, 2001
  • Published electronically: March 7, 2002
  • Additional Notes: Partially supported by NSF grant DMS-9970725 and MONTS-190729.
  • © Copyright 2002 Jaroslaw Kwapisz
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2865-2895
  • MSC (1991): Primary 37E45, 37E30
  • DOI: https://doi.org/10.1090/S0002-9947-02-02952-5
  • MathSciNet review: 1895207